There were plenty of Swedes near the top of the leaderboard with Christopher Hanell, Henrik Stenson and Wilhelm Schauman at 4-under-par 68 along with Englishmen Steve Webster and Chris Gane.
Howell, who has missed the cut in each of his last two events, played the back side first at Barsebck Golf & Country Club and jumped out of the gate with a birdie at the 10th, his first. Howell then birdied the 12th and added a birdie at the 14th to move to 3 under.
The 29-year-old continued his fine play on the back nine with two straight birdies starting at the 16th to go out in 31.
Howell cooled off on the front side, but tallied a birdie at the par-3 eighth to move to minus-6. He stumbled with a bogey at the par-5 ninth, however, to hold a share of the lead.
'Everything went nicely for me early on and no mistakes until on the last there, but that's golf sometimes,' said Howell, who has six top-10 finishes this season. 'Frustrating, but I could have bogeyed the first, it just happened to be the last.'
Edfors also started on the 10th and parred his opening hole before running off three consecutive birdies starting at the 11th. Edfors faltered with a bogey at the 15th, but came right back with a birdie at the 17th.
The 28-year-old, who earned his card through the Challenge Tour, drained a 10-foot putt for a birdie at the fourth and knocked his tee shot inside 3 feet at the par-3 eighth. Edfors converted the short birdie putt to join Howell in the clubhouse at 5 under.
Jesper Parnevik, a two-time winner of this event, shares eighth place with Luke Donald, Thomas Levet, Paul McGinley, Soren Hansen and Sebastien Fernandez at 3-under-par 69.
Graeme McDowell, the 2002 champion at Kungsngen, followed in a group at 2-under-par 70.
Defending champion Adam Scott started on the 10th and had a rough first nine with back-to-back bogeys to open his round. The young Australian responded with three straight birdies from the 12th but have a shot back with a bogey at the 16th.
Scott then birdied the 17th before finding trouble with a double-bogey at the very next hole. He managed a birdie at the second en route to a 72 to finish five shots back in a group that features former Scandinavian Masters champions Colin Montgomerie and Lee Westwood.